4.
\(\left\{{}\begin{matrix}0< x< \dfrac{\pi}{2}\\sinx=\dfrac{1}{2}\end{matrix}\right.\) \(\Rightarrow x=\dfrac{\pi}{6}\)
\(\left\{{}\begin{matrix}\dfrac{\pi}{2}< y< \pi\\cosy=-\dfrac{1}{2}\end{matrix}\right.\) \(\Rightarrow y=\dfrac{2\pi}{3}\)
\(\Rightarrow P=sin\left(\dfrac{\pi}{6}+\dfrac{2\pi}{3}\right)-sin\left(\dfrac{\pi}{6}-\dfrac{2\pi}{3}\right)=\dfrac{3}{2}\)
5.
\(\dfrac{cos4x+cos2x+1}{sin4x+sin2x}=\dfrac{2cos^22x-1+cos2x+1}{2sin2x.cos2x+sin2x}=\dfrac{2cos2x\left(cos2x+1\right)}{2sin2x\left(cos2x+1\right)}\)
\(=\dfrac{cos2x}{sin2x}=cot2x\)
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